Monoenergetic beam of electrons moving along + y direction enters a region of uniform electric and m

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8.Electromagnetic waves

medium

The monoenergetic beam of electrons moving along $+ y$ direction enters a region of uniform electric and magnetic fields. If the beam goes straight undeflected, then fields $B$ and $E$ are directed respectively along

$- y$ axis and $- z$ axis

$+ z$ axis and $+ x$ axis

$+ x$ axis and $+ z$ axis

$- x$ axis and $- y$ axis

Solution

The total Lorentz force on the electron is

$\overrightarrow{\mathrm{F}}=-e(\overrightarrow{\mathrm{E}}+\vec{v} \times \overrightarrow{\mathrm{B}})$

The electron will be undeflected if $\mathrm{v} \perp \mathrm{B}.$

If $\mathrm{E}$ is along $+\mathrm{z}$ -direction, the force $-\mathrm{e}$ $\mathrm{E}$ will be along $\mathrm{z}$ -direction. If $\mathrm{B}$ is along $+\mathrm{x}$ direction, force

$-\mathrm{e}(\mathrm{v} \times \mathrm{B})$ will be along $+\mathrm{z}$ divection. When $\mathrm{eE}$ $=$ $\mathrm{evB}.$ the electron moves along $+\mathrm{y}$ -direction undeflected. Hence the correct choice is $(3).$

Thus, for an electron moving along $+$ $\mathrm{y}$ direction. the electric field should be along $+\mathrm{z}$ direction and magnetic field along $+\mathrm{x}$ direction, then the electron will be undeflected.

Standard 12

Physics

Which of the following is $NOT$ true for electromagnetic waves ?

easy

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by ${E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .$ The dielectric constant of the medium is equal to :

(Take $\mu_{{r}}=1$ )

hard

(JEE MAIN-2021)

In a certain region uniform electric field $E$ and magnetic field $B$ are present in the opposite direction. At the instant $t = 0,$ a particle of mass $m$ carrying a charge $q$ is given velocity $v_o$ at an angle $\theta ,$ with the $y$ axis, in the $yz$ plane. The time after which the speed of the particle would be minimum is equal to

medium

Suppose that the electric field part of an electromagnetic wave in vacuum is

$E =\left\{(3.1 \;N / C ) \text { cos }\left[(1.8 \;rad / m ) y+\left(5.4 \times 10^{6} \;rad / s \right) t\right]\right\} \hat{ i }$

$(a)$ What is the direction of propagation?

$(b)$ What is the wavelength $\lambda$ ?

$(c)$ What is the frequency $v ?$

$(d)$ What is the amplitude of the magnetic field part of the wave?

$(e)$ Write an expression for the magnetic field part of the wave.

medium

The velocity of electromagnetic radiation in a medium of permittivity ${\varepsilon _0}$ and permeability ${\mu _0}$ is given by

easy

(AIPMT-2008)

The monoenergetic beam of electrons moving along $+ y$ direction enters a region of uniform electric and magnetic fields. If the beam goes straight undeflected, then fields $B$ and $E$ are directed respectively along

Solution

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Which of the following is $NOT$ true for electromagnetic waves ?

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by ${E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .$ The dielectric constant of the medium is equal to : (Take $\mu_{{r}}=1$ )

The velocity of electromagnetic radiation in a medium of permittivity ${\varepsilon _0}$ and permeability ${\mu _0}$ is given by

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Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by ${E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .$ The dielectric constant of the medium is equal to :

(Take $\mu_{{r}}=1$ )